Non-local Matching Condition and Scale-invariant Spectrum in Bouncing Cosmology

TL;DR

This paper proves that local causality constraints prevent scale-invariant spectra in bouncing cosmologies, but nonlocal effects inspired by noncommutative geometry can produce such spectra consistent with observations.

Contribution

It introduces a local causality framework to analyze matching conditions in bouncing cosmology and demonstrates that nonlocal effects can generate scale-invariant spectra.

Findings

A no-go theorem shows local causality forbids scale invariance in bouncing scenarios.

Nonlocal effects can produce scale-invariant spectra compatible with observations.

The bounce energy scale is below the Planck scale, aligning with empirical data.

Abstract

In cosmological scenarios such as the pre-big bang scenario or the ekpyrotic scenario, a matching condition between the metric perturbations in the pre-big bang phase and those in the post big-bang phase is often assumed. Various matching conditions have been considered in the literature. Nevertheless obtaining a scale invariant CMB spectrum via a concrete mechanism remains impossible. In this paper, we examine this problem from the point of view of local causality. We begin with introducing the notion of local causality and explain how it constrains the form of the matching condition. We then prove a no-go theorem: independent of the details of the matching condition, a scale invariant spectrum is impossible as long as the local causality condition is satisfied. In our framework, it is easy to show that a violation of local causality around the bounce is needed in order to give a scale invariant spectrum. We study a specific scenario of this possibility by considering a nonlocal effective theory inspired by noncommutative geometry around the bounce and show that a scale invariant spectrum is possible. Moreover we demonstrate that the magnitude of the spectrum is compatible with observations if the bounce is assumed to occur at an energy scale which is a few orders of magnitude below the Planckian energy scale.